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## Main Question or Discussion Point

Hello,

In a book I'm reading about linear algebra it's mentioned that in order for the homogeneous system

Ax = 0

to have a solution (other than the trivial solution) the coefficient Matrix must be singular.

The thing is, I can't remember (the wikipedia page on homogeneous systems didn't turn up anything) why if A is invertible, then the system does not have non-zero solutions.

Any help on why this is so is appreciated.

Thank you in advance

In a book I'm reading about linear algebra it's mentioned that in order for the homogeneous system

Ax = 0

to have a solution (other than the trivial solution) the coefficient Matrix must be singular.

The thing is, I can't remember (the wikipedia page on homogeneous systems didn't turn up anything) why if A is invertible, then the system does not have non-zero solutions.

Any help on why this is so is appreciated.

Thank you in advance

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